%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP764-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:41:12 PM UTC 2026
% Result : Unsatisfiable 45.78s 8.57s
% Output : CNFRefutation 45.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 13
% Syntax : Number of clauses : 246 ( 246 unt; 0 nHn; 6 RR)
% Number of literals : 246 ( 245 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 431 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos07,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos02,axiom,
product(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(sos08,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(goals,negated_conjecture,
product(x0,product(eta(x0),x1)) != product(j(j(x0)),x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(sos12,axiom,
eta(X1) = product(i(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
cnf(c_0_13,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_14,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_15,plain,
quotient(product(difference(X1,X2),product(X3,X1)),X1) = difference(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_17,plain,
difference(X1,product(X2,quotient(X3,X1))) = quotient(product(difference(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
product(one,X1) = X1,
sos02 ).
cnf(c_0_19,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_20,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_21,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_22,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
sos08 ).
cnf(c_0_23,plain,
quotient(product(difference(X1,one),X2),X1) = difference(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_25,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_26,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_27,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_28,plain,
difference(one,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_29,plain,
difference(X1,product(quotient(X1,X2),product(X2,X3))) = quotient(quotient(product(X3,X1),X2),quotient(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_30,plain,
difference(X1,quotient(one,X1)) = quotient(difference(X1,one),X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_32,plain,
product(difference(X1,product(X2,X3)),X1) = product(difference(X1,X2),product(X3,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_33,plain,
difference(difference(X1,one),product(X1,quotient(one,X1))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
quotient(quotient(X1,X2),quotient(one,X2)) = product(quotient(one,X2),product(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24]) ).
cnf(c_0_35,plain,
quotient(difference(difference(X1,one),one),difference(X1,one)) = difference(difference(X1,one),X1),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
product(difference(difference(X1,one),X1),product(quotient(one,X1),difference(X1,one))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_14]) ).
cnf(c_0_37,plain,
quotient(difference(difference(X1,one),X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_31]),c_0_31]),c_0_14]),c_0_24]) ).
cnf(c_0_38,plain,
quotient(X1,X1) = one,
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_39,plain,
difference(difference(difference(X1,one),X1),one) = product(quotient(one,X1),difference(X1,one)),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_40,plain,
difference(difference(X1,one),X1) = product(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_37]) ).
cnf(c_0_41,plain,
product(quotient(one,X1),product(X1,X1)) = quotient(one,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_42,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_43,plain,
product(quotient(one,X1),difference(X1,one)) = difference(product(X1,X1),one),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
quotient(X1,quotient(one,X1)) = product(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_41]),c_0_30]),c_0_42]) ).
cnf(c_0_45,plain,
product(quotient(one,X1),quotient(one,quotient(one,X1))) = product(X1,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_42]) ).
cnf(c_0_46,plain,
difference(quotient(one,X1),difference(product(X1,X1),one)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_47,plain,
product(difference(X1,one),difference(X1,one)) = quotient(difference(X1,one),X1),
inference(spm,[status(thm)],[c_0_44,c_0_31]) ).
cnf(c_0_48,plain,
difference(quotient(difference(X1,one),X1),one) = product(quotient(one,quotient(one,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_30]) ).
cnf(c_0_49,plain,
difference(quotient(one,X1),product(X1,quotient(one,X1))) = quotient(one,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
cnf(c_0_50,plain,
difference(X1,product(quotient(one,quotient(one,X1)),X1)) = difference(difference(X1,one),one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_31]),c_0_48]) ).
cnf(c_0_51,plain,
product(difference(quotient(one,X1),X1),product(quotient(one,X1),quotient(one,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_49]),c_0_16]) ).
cnf(c_0_52,plain,
product(quotient(one,quotient(one,X1)),X1) = product(X1,difference(difference(X1,one),one)),
inference(spm,[status(thm)],[c_0_14,c_0_50]) ).
cnf(c_0_53,plain,
product(X1,quotient(product(X2,product(X3,X1)),X1)) = product(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_54,plain,
quotient(one,product(quotient(one,X1),quotient(one,X1))) = difference(quotient(one,X1),X1),
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_55,plain,
product(quotient(one,X1),quotient(one,X1)) = quotient(difference(X1,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_30]) ).
cnf(c_0_56,plain,
difference(quotient(difference(X1,one),X1),one) = product(X1,difference(difference(X1,one),one)),
inference(rw,[status(thm)],[c_0_48,c_0_52]) ).
cnf(c_0_57,plain,
product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_53,c_0_16]) ).
cnf(c_0_58,plain,
quotient(product(X1,quotient(one,X1)),X1) = difference(X1,one),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_59,plain,
quotient(one,quotient(difference(X1,one),X1)) = difference(quotient(one,X1),X1),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
product(difference(X1,difference(X1,one)),product(X1,X1)) = one,
inference(spm,[status(thm)],[c_0_51,c_0_31]) ).
cnf(c_0_61,plain,
product(quotient(difference(X1,one),X1),difference(quotient(one,X1),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_56]),c_0_57]),c_0_27]),c_0_31]),c_0_27]),c_0_58]),c_0_14]),c_0_59]) ).
cnf(c_0_62,plain,
difference(X1,difference(X1,one)) = quotient(one,product(X1,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_60]) ).
cnf(c_0_63,plain,
product(product(X1,quotient(X2,product(X3,X1))),X3) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_53,c_0_16]) ).
cnf(c_0_64,plain,
product(product(X1,X1),quotient(one,product(X1,X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_35]),c_0_40]),c_0_62]) ).
cnf(c_0_65,plain,
quotient(product(X1,quotient(X2,X1)),X3) = product(X1,quotient(X2,product(X3,X1))),
inference(spm,[status(thm)],[c_0_25,c_0_63]) ).
cnf(c_0_66,plain,
difference(product(X1,X1),one) = quotient(one,product(X1,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_67,plain,
product(X1,quotient(product(difference(X1,X2),X3),X1)) = product(X2,quotient(X3,X1)),
inference(spm,[status(thm)],[c_0_57,c_0_14]) ).
cnf(c_0_68,plain,
product(X1,quotient(X1,product(X2,X1))) = quotient(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_38]),c_0_24]) ).
cnf(c_0_69,plain,
product(quotient(one,X1),difference(X1,one)) = quotient(one,product(X1,X1)),
inference(rw,[status(thm)],[c_0_43,c_0_66]) ).
cnf(c_0_70,plain,
quotient(difference(X1,one),quotient(one,product(X1,X1))) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_62]) ).
cnf(c_0_71,plain,
product(X1,quotient(product(X2,X1),product(X3,X1))) = quotient(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_65,c_0_25]) ).
cnf(c_0_72,plain,
product(X1,quotient(difference(difference(X2,X1),X3),X2)) = product(X2,quotient(X3,X2)),
inference(spm,[status(thm)],[c_0_67,c_0_14]) ).
cnf(c_0_73,plain,
quotient(difference(X1,one),quotient(one,X1)) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_27]) ).
cnf(c_0_74,plain,
quotient(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_71,c_0_16]) ).
cnf(c_0_75,plain,
quotient(product(X1,product(difference(product(X2,X1),X3),X2)),X2) = difference(X2,X3),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_76,plain,
quotient(difference(difference(X1,one),X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_72]) ).
cnf(c_0_77,plain,
product(X1,quotient(quotient(one,X1),X1)) = difference(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_73]),c_0_57]),c_0_24]) ).
cnf(c_0_78,plain,
product(X1,quotient(product(difference(X1,X2),X1),X3)) = quotient(X2,quotient(X3,X1)),
inference(spm,[status(thm)],[c_0_74,c_0_14]) ).
cnf(c_0_79,plain,
quotient(X1,one) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_80,plain,
product(X1,product(difference(product(X2,X1),X3),X2)) = product(difference(X2,X3),X2),
inference(spm,[status(thm)],[c_0_16,c_0_75]) ).
cnf(c_0_81,plain,
product(product(X1,quotient(X2,X1)),X1) = difference(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_16,c_0_76]) ).
cnf(c_0_82,plain,
product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_67,c_0_24]) ).
cnf(c_0_83,plain,
difference(X1,quotient(product(X1,X2),X3)) = quotient(product(X2,X1),product(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_71]) ).
cnf(c_0_84,plain,
quotient(quotient(one,X1),X1) = quotient(one,product(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_77]),c_0_62]) ).
cnf(c_0_85,plain,
product(X1,product(difference(X1,X2),X1)) = quotient(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,plain,
difference(X1,product(difference(X2,X3),X2)) = product(difference(product(X2,X1),X3),X2),
inference(spm,[status(thm)],[c_0_26,c_0_80]) ).
cnf(c_0_87,plain,
difference(difference(X1,one),difference(X1,X2)) = product(product(X2,quotient(one,X1)),X1),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,plain,
difference(difference(X1,X2),difference(X1,product(X2,X3))) = quotient(product(product(X3,X1),difference(X1,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_15]),c_0_14]) ).
cnf(c_0_89,plain,
difference(difference(X1,one),product(difference(X1,X2),X3)) = product(product(X2,quotient(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_81,c_0_67]) ).
cnf(c_0_90,plain,
difference(quotient(one,X1),X1) = quotient(X1,difference(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_31]),c_0_47]),c_0_59]) ).
cnf(c_0_91,plain,
product(X1,quotient(quotient(X2,quotient(one,X1)),X1)) = product(product(X1,X1),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_53,c_0_85]) ).
cnf(c_0_92,plain,
product(product(difference(product(X1,X2),X3),X1),X2) = product(difference(X2,difference(X1,X3)),product(X1,X2)),
inference(spm,[status(thm)],[c_0_32,c_0_86]) ).
cnf(c_0_93,plain,
product(product(X1,quotient(one,X2)),X2) = product(product(X1,X2),difference(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_79]),c_0_18]) ).
cnf(c_0_94,plain,
difference(X1,product(quotient(X1,difference(X1,one)),X2)) = product(product(X1,X1),difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_42]),c_0_57]),c_0_24]),c_0_91]) ).
cnf(c_0_95,plain,
difference(X1,difference(quotient(one,X1),X2)) = product(product(X2,X1),difference(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_16]),c_0_28]),c_0_16]),c_0_24]) ).
cnf(c_0_96,plain,
difference(X1,quotient(X1,X2)) = quotient(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_68]) ).
cnf(c_0_97,plain,
product(X1,product(product(X1,X1),difference(X1,X2))) = product(quotient(X1,difference(X1,one)),X2),
inference(spm,[status(thm)],[c_0_14,c_0_94]) ).
cnf(c_0_98,plain,
product(X1,product(product(X2,X1),difference(X1,one))) = difference(quotient(one,X1),X2),
inference(spm,[status(thm)],[c_0_14,c_0_95]) ).
cnf(c_0_99,plain,
product(product(product(X1,X2),X1),difference(X1,one)) = difference(difference(X1,one),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_57]),c_0_24]),c_0_81]) ).
cnf(c_0_100,plain,
quotient(X1,product(difference(X2,X1),X1)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_96,c_0_31]) ).
cnf(c_0_101,plain,
product(X1,quotient(one,product(X1,X1))) = difference(X1,one),
inference(spm,[status(thm)],[c_0_14,c_0_62]) ).
cnf(c_0_102,plain,
product(quotient(one,product(X1,X1)),X1) = quotient(one,X1),
inference(spm,[status(thm)],[c_0_16,c_0_84]) ).
cnf(c_0_103,plain,
product(difference(X1,quotient(X2,X3)),product(X3,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_104,plain,
product(difference(X1,one),product(X2,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_105,plain,
product(quotient(X1,difference(X1,one)),product(X1,X2)) = product(X1,product(product(X1,X1),X2)),
inference(spm,[status(thm)],[c_0_97,c_0_26]) ).
cnf(c_0_106,plain,
difference(X1,product(X2,quotient(X3,X2))) = quotient(difference(difference(X2,X1),X3),X2),
inference(spm,[status(thm)],[c_0_26,c_0_72]) ).
cnf(c_0_107,plain,
difference(quotient(one,X1),product(X1,X2)) = product(X1,difference(difference(X1,one),X2)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_108,plain,
difference(difference(X1,X2),X1) = product(difference(X2,X1),X1),
inference(spm,[status(thm)],[c_0_42,c_0_100]) ).
cnf(c_0_109,plain,
difference(X1,quotient(difference(X1,one),X2)) = quotient(quotient(one,X1),product(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_101]),c_0_102]) ).
cnf(c_0_110,plain,
quotient(product(difference(X1,X2),X1),product(X3,X1)) = difference(X1,quotient(X2,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_103]) ).
cnf(c_0_111,plain,
quotient(X1,product(X1,X1)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_112,plain,
product(difference(X1,quotient(X2,X1)),X1) = product(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_104,c_0_16]) ).
cnf(c_0_113,plain,
quotient(quotient(X1,difference(X2,one)),X2) = product(X2,product(difference(X2,one),X1)),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_114,plain,
product(product(X1,quotient(X2,difference(X2,one))),X2) = product(product(X1,X2),product(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_105]),c_0_53]) ).
cnf(c_0_115,plain,
quotient(product(product(X1,X2),difference(X2,one)),X2) = product(X1,quotient(one,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_88]),c_0_79]),c_0_18]),c_0_82]) ).
cnf(c_0_116,plain,
quotient(difference(quotient(difference(X1,one),X1),X2),X1) = product(X1,difference(difference(X1,one),quotient(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_30]) ).
cnf(c_0_117,plain,
difference(quotient(quotient(one,X1),product(X2,X1)),X1) = product(difference(quotient(difference(X1,one),X2),X1),X1),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_118,plain,
quotient(X1,quotient(X2,X1)) = product(X1,quotient(X1,X2)),
inference(spm,[status(thm)],[c_0_68,c_0_16]) ).
cnf(c_0_119,plain,
difference(X1,quotient(X2,quotient(X3,X1))) = quotient(product(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_110,c_0_16]) ).
cnf(c_0_120,plain,
product(quotient(one,product(X1,X1)),product(product(X1,X1),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_111]),c_0_70]) ).
cnf(c_0_121,plain,
difference(quotient(one,quotient(one,X1)),product(X1,quotient(one,X1))) = quotient(one,quotient(one,quotient(one,X1))),
inference(spm,[status(thm)],[c_0_49,c_0_45]) ).
cnf(c_0_122,plain,
product(difference(X1,one),quotient(X2,difference(X1,one))) = product(product(difference(X1,one),X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_26]) ).
cnf(c_0_123,plain,
quotient(product(product(X1,X2),product(X2,X2)),X2) = product(X1,quotient(X2,difference(X2,one))),
inference(spm,[status(thm)],[c_0_25,c_0_114]) ).
cnf(c_0_124,plain,
quotient(product(X1,difference(X2,one)),X2) = product(quotient(X1,X2),quotient(one,X2)),
inference(spm,[status(thm)],[c_0_115,c_0_16]) ).
cnf(c_0_125,plain,
quotient(difference(product(X1,X1),one),difference(X1,one)) = quotient(one,X1),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_126,plain,
quotient(difference(product(X1,X1),X2),quotient(one,X1)) = product(quotient(one,X1),product(difference(X1,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_28]),c_0_42]),c_0_24]),c_0_79]),c_0_24]),c_0_118]),c_0_79]),c_0_79]),c_0_24]),c_0_79]),c_0_24]),c_0_28]),c_0_42]),c_0_24]),c_0_79]),c_0_24]),c_0_119]),c_0_79]) ).
cnf(c_0_127,plain,
quotient(product(X1,product(X2,quotient(X3,X1))),quotient(X3,X1)) = difference(quotient(X3,X1),product(X3,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_128,plain,
difference(quotient(one,product(X1,X1)),X1) = product(product(X1,X1),X1),
inference(spm,[status(thm)],[c_0_26,c_0_120]) ).
cnf(c_0_129,plain,
difference(X1,quotient(difference(X1,one),X1)) = quotient(quotient(difference(X1,one),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_55]),c_0_30]),c_0_24]) ).
cnf(c_0_130,plain,
quotient(difference(difference(X1,one),one),difference(X1,one)) = product(X1,X1),
inference(rw,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_131,plain,
product(difference(quotient(one,quotient(one,X1)),X1),product(X1,quotient(one,X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_121]),c_0_16]),c_0_45]) ).
cnf(c_0_132,plain,
product(product(difference(X1,one),product(product(X2,X1),X3)),X1) = product(product(difference(X1,X2),X1),quotient(X3,difference(X1,one))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_104]),c_0_122]) ).
cnf(c_0_133,plain,
product(X1,product(X2,quotient(X1,difference(X1,one)))) = product(product(X1,product(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_53,c_0_123]) ).
cnf(c_0_134,plain,
product(difference(X1,one),product(X2,difference(X1,one))) = difference(X1,quotient(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_124]),c_0_17]),c_0_24]),c_0_16]) ).
cnf(c_0_135,plain,
quotient(difference(X1,one),difference(difference(X1,one),one)) = quotient(one,product(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_31]),c_0_62]) ).
cnf(c_0_136,plain,
quotient(quotient(one,product(X1,X1)),difference(X1,one)) = quotient(one,X1),
inference(rw,[status(thm)],[c_0_125,c_0_66]) ).
cnf(c_0_137,plain,
product(product(difference(X1,X2),X1),quotient(one,X1)) = product(X1,difference(product(X1,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_126]),c_0_26]),c_0_42]) ).
cnf(c_0_138,plain,
difference(product(X1,quotient(X2,X3)),product(X1,X2)) = quotient(difference(quotient(X2,X3),product(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_127]) ).
cnf(c_0_139,plain,
quotient(product(difference(X1,X2),X1),product(X2,X1)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_25,c_0_104]) ).
cnf(c_0_140,plain,
product(product(product(X1,X1),X1),difference(X1,one)) = product(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_64]),c_0_42]),c_0_24]),c_0_32]),c_0_128]),c_0_101]) ).
cnf(c_0_141,plain,
difference(difference(X1,one),product(X1,X1)) = quotient(product(X1,X1),difference(X1,one)),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_142,plain,
quotient(product(X1,X1),difference(X1,one)) = product(product(X1,X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_111]),c_0_25]) ).
cnf(c_0_143,plain,
product(X1,difference(difference(X1,one),one)) = difference(quotient(one,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_61]),c_0_48]),c_0_52]) ).
cnf(c_0_144,plain,
difference(quotient(one,quotient(one,X1)),X1) = quotient(one,product(X1,quotient(one,X1))),
inference(spm,[status(thm)],[c_0_25,c_0_131]) ).
cnf(c_0_145,plain,
product(product(difference(X1,X2),difference(X1,one)),X1) = product(X1,difference(product(X1,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_134]),c_0_25]),c_0_135]),c_0_136]),c_0_137]) ).
cnf(c_0_146,plain,
difference(product(X1,X2),product(X1,X3)) = quotient(difference(X2,product(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_138,c_0_31]) ).
cnf(c_0_147,plain,
difference(difference(quotient(one,X1),X1),one) = product(quotient(one,X1),quotient(one,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_51]) ).
cnf(c_0_148,plain,
quotient(product(product(X1,X1),X1),product(X1,X1)) = difference(difference(X1,one),one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_32]),c_0_141]),c_0_142]),c_0_14]),c_0_24]) ).
cnf(c_0_149,plain,
product(X1,difference(difference(X1,one),one)) = quotient(X1,difference(X1,one)),
inference(rw,[status(thm)],[c_0_143,c_0_90]) ).
cnf(c_0_150,plain,
product(quotient(one,quotient(one,X1)),X1) = difference(quotient(one,X1),X1),
inference(rw,[status(thm)],[c_0_52,c_0_143]) ).
cnf(c_0_151,plain,
quotient(difference(difference(X1,one),one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_31]),c_0_27]) ).
cnf(c_0_152,plain,
difference(quotient(one,X1),difference(X1,one)) = quotient(one,product(X1,quotient(one,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_31]),c_0_27]) ).
cnf(c_0_153,plain,
product(product(X1,difference(X2,one)),X2) = product(product(X1,X2),quotient(one,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_26]),c_0_146]),c_0_82]) ).
cnf(c_0_154,plain,
difference(difference(quotient(one,X1),X1),one) = quotient(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_147,c_0_55]) ).
cnf(c_0_155,plain,
difference(quotient(difference(X1,one),X1),X1) = product(quotient(X1,difference(X1,one)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_30]),c_0_90]) ).
cnf(c_0_156,plain,
product(quotient(X1,difference(X1,one)),X1) = product(X1,product(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_148]),c_0_143]),c_0_90]),c_0_25]) ).
cnf(c_0_157,plain,
quotient(X1,product(X1,quotient(one,X1))) = difference(difference(X1,one),one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_149]),c_0_96]),c_0_27]) ).
cnf(c_0_158,plain,
product(quotient(one,quotient(one,X1)),X1) = quotient(X1,difference(X1,one)),
inference(rw,[status(thm)],[c_0_150,c_0_90]) ).
cnf(c_0_159,plain,
product(product(X1,quotient(one,X1)),X1) = difference(difference(X1,one),one),
inference(spm,[status(thm)],[c_0_16,c_0_151]) ).
cnf(c_0_160,plain,
difference(X1,difference(difference(X1,one),one)) = quotient(one,product(X1,quotient(one,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_31]),c_0_27]) ).
cnf(c_0_161,plain,
product(quotient(product(X1,X2),product(X2,X2)),X2) = product(difference(X2,one),product(X2,X1)),
inference(spm,[status(thm)],[c_0_112,c_0_83]) ).
cnf(c_0_162,plain,
quotient(product(difference(X1,one),product(X1,X2)),X2) = quotient(product(X1,product(quotient(one,X1),X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_153]),c_0_13]) ).
cnf(c_0_163,plain,
quotient(product(difference(X1,X2),X2),difference(X2,X1)) = product(product(difference(X1,X2),X2),difference(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_100]),c_0_25]) ).
cnf(c_0_164,plain,
difference(product(X1,quotient(one,X1)),difference(difference(X1,one),one)) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_151]) ).
cnf(c_0_165,plain,
difference(X1,product(X2,quotient(one,X2))) = product(difference(product(X2,X1),one),X2),
inference(spm,[status(thm)],[c_0_86,c_0_27]) ).
cnf(c_0_166,plain,
difference(quotient(X1,difference(X1,one)),one) = quotient(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_154,c_0_90]) ).
cnf(c_0_167,plain,
difference(quotient(difference(X1,one),X1),X1) = product(X1,product(X1,X1)),
inference(rw,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_168,plain,
difference(product(X1,X1),quotient(one,X2)) = quotient(one,product(X2,product(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_64]),c_0_16]) ).
cnf(c_0_169,plain,
product(difference(difference(X1,one),one),product(X1,quotient(one,X1))) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_157]) ).
cnf(c_0_170,plain,
product(X1,product(X1,quotient(one,X1))) = quotient(one,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_158]),c_0_113]),c_0_27]) ).
cnf(c_0_171,plain,
quotient(quotient(one,quotient(one,X1)),X1) = quotient(one,product(X1,quotient(one,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_159]),c_0_160]),c_0_41]) ).
cnf(c_0_172,plain,
product(difference(X1,one),product(X1,quotient(X2,X1))) = product(quotient(X2,product(X1,X1)),X1),
inference(spm,[status(thm)],[c_0_161,c_0_16]) ).
cnf(c_0_173,plain,
product(difference(X1,one),product(X1,X2)) = product(X1,product(quotient(one,X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_162]),c_0_16]) ).
cnf(c_0_174,plain,
quotient(quotient(X1,difference(X1,one)),difference(X1,one)) = product(X1,product(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_143]),c_0_90]),c_0_165]),c_0_143]),c_0_90]),c_0_166]),c_0_16]),c_0_143]),c_0_90]),c_0_156]) ).
cnf(c_0_175,plain,
product(quotient(one,X1),quotient(difference(X1,one),X1)) = quotient(one,product(X1,product(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_42]),c_0_118]),c_0_79]),c_0_55]),c_0_168]) ).
cnf(c_0_176,plain,
quotient(difference(difference(X1,X2),product(X3,X1)),X1) = difference(X2,product(X1,X3)),
inference(spm,[status(thm)],[c_0_146,c_0_14]) ).
cnf(c_0_177,plain,
difference(product(X1,quotient(one,X1)),one) = quotient(one,product(X1,quotient(one,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_169]),c_0_164]),c_0_170]),c_0_171]) ).
cnf(c_0_178,plain,
product(X1,product(quotient(one,X1),quotient(X2,X1))) = product(quotient(X2,product(X1,X1)),X1),
inference(rw,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_179,plain,
quotient(quotient(one,X1),quotient(X2,X1)) = product(X1,quotient(difference(X1,one),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_30]),c_0_16]) ).
cnf(c_0_180,plain,
quotient(quotient(one,product(X1,X1)),X1) = quotient(one,product(X1,product(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_42]),c_0_84]),c_0_55]),c_0_175]) ).
cnf(c_0_181,plain,
difference(difference(X1,X2),product(X3,X1)) = product(difference(X2,product(X1,X3)),X1),
inference(spm,[status(thm)],[c_0_16,c_0_176]) ).
cnf(c_0_182,plain,
product(quotient(one,product(X1,quotient(one,X1))),X1) = quotient(one,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_169]),c_0_164]),c_0_170]),c_0_177]) ).
cnf(c_0_183,plain,
product(X1,quotient(one,product(X1,quotient(one,X1)))) = difference(difference(X1,one),one),
inference(spm,[status(thm)],[c_0_14,c_0_160]) ).
cnf(c_0_184,plain,
difference(X1,product(quotient(X2,product(X1,X1)),X1)) = product(quotient(one,X1),quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_178]) ).
cnf(c_0_185,plain,
difference(product(X1,X2),product(product(X1,X3),X4)) = quotient(difference(X2,product(X3,product(X4,X1))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_53]),c_0_16]) ).
cnf(c_0_186,plain,
product(product(X1,X1),quotient(one,product(X1,product(X1,X1)))) = quotient(one,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_111]),c_0_136]),c_0_66]),c_0_180]) ).
cnf(c_0_187,plain,
product(quotient(one,product(X1,product(X1,X1))),X1) = quotient(one,product(X1,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_180]) ).
cnf(c_0_188,plain,
product(quotient(one,X1),product(X1,X2)) = product(X1,product(difference(X1,one),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_112]),c_0_34]) ).
cnf(c_0_189,plain,
difference(difference(X1,X2),quotient(one,quotient(one,X1))) = product(difference(X2,difference(difference(X1,one),one)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_183]) ).
cnf(c_0_190,plain,
difference(X1,product(difference(X1,one),X2)) = product(quotient(one,X1),difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_110]),c_0_112]),c_0_25]) ).
cnf(c_0_191,plain,
difference(product(X1,X2),quotient(one,X1)) = quotient(difference(X2,difference(X1,one)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_187]),c_0_101]) ).
cnf(c_0_192,plain,
difference(product(X1,X2),difference(X1,one)) = quotient(difference(X2,quotient(one,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_101]),c_0_102]) ).
cnf(c_0_193,plain,
product(product(X1,product(difference(X1,one),X2)),X1) = quotient(X2,difference(X1,one)),
inference(spm,[status(thm)],[c_0_16,c_0_113]) ).
cnf(c_0_194,plain,
product(X1,product(difference(X1,one),difference(X1,X2))) = product(quotient(one,X1),X2),
inference(spm,[status(thm)],[c_0_188,c_0_14]) ).
cnf(c_0_195,plain,
quotient(product(difference(X1,X2),X2),quotient(one,X2)) = product(quotient(difference(X1,X2),difference(X2,one)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_191]),c_0_42]),c_0_108]),c_0_192]),c_0_31]) ).
cnf(c_0_196,plain,
quotient(difference(X1,X2),difference(X1,one)) = product(product(quotient(one,X1),X2),X1),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_197,plain,
difference(X1,product(quotient(one,X1),X2)) = product(difference(X1,one),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_194]) ).
cnf(c_0_198,plain,
quotient(product(product(X1,X2),X3),quotient(X4,X1)) = product(X1,quotient(product(X2,product(X3,X1)),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_53]),c_0_16]) ).
cnf(c_0_199,plain,
quotient(product(X1,X2),quotient(one,X2)) = product(quotient(X1,difference(X2,one)),X2),
inference(spm,[status(thm)],[c_0_195,c_0_42]) ).
cnf(c_0_200,plain,
difference(difference(X1,one),product(quotient(one,X1),X2)) = product(difference(difference(X1,one),one),difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_196]),c_0_181]),c_0_28]),c_0_99]) ).
cnf(c_0_201,plain,
product(X1,product(quotient(one,X1),difference(X1,X2))) = product(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_173,c_0_14]) ).
cnf(c_0_202,plain,
difference(X1,product(quotient(one,quotient(one,X1)),X2)) = product(difference(X1,one),difference(quotient(one,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_194]),c_0_42]),c_0_26]) ).
cnf(c_0_203,plain,
product(quotient(product(X1,X2),difference(X1,one)),X1) = product(X1,product(X2,product(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_79]) ).
cnf(c_0_204,plain,
difference(difference(X1,one),product(X1,X2)) = product(X1,difference(quotient(one,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_42]),c_0_202]),c_0_173]),c_0_31]),c_0_173]),c_0_14]) ).
cnf(c_0_205,plain,
product(X1,quotient(product(X2,product(difference(X1,X3),product(X4,X1))),X1)) = product(product(X1,X2),difference(X1,product(X3,X4))),
inference(spm,[status(thm)],[c_0_57,c_0_15]) ).
cnf(c_0_206,plain,
quotient(product(X1,product(X2,product(X1,X1))),X1) = quotient(product(X1,X2),difference(X1,one)),
inference(spm,[status(thm)],[c_0_25,c_0_203]) ).
cnf(c_0_207,plain,
product(X1,difference(quotient(one,X1),difference(X1,X2))) = difference(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_204,c_0_14]) ).
cnf(c_0_208,plain,
product(quotient(quotient(X1,X2),product(X2,X2)),X2) = quotient(X1,quotient(X2,difference(X2,one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_124]),c_0_76]),c_0_57]),c_0_24]),c_0_172]) ).
cnf(c_0_209,plain,
product(product(X1,X1),difference(X1,product(X2,X1))) = product(X1,quotient(X2,difference(X1,one))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_14]) ).
cnf(c_0_210,plain,
product(difference(X1,X2),product(difference(X2,X3),X1)) = product(difference(X1,X3),X1),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_211,plain,
difference(quotient(one,X1),difference(X1,X2)) = difference(X1,difference(difference(X1,one),X2)),
inference(spm,[status(thm)],[c_0_26,c_0_207]) ).
cnf(c_0_212,plain,
difference(difference(X1,one),difference(X1,X2)) = product(product(X2,X1),difference(X1,one)),
inference(rw,[status(thm)],[c_0_87,c_0_93]) ).
cnf(c_0_213,plain,
difference(X1,quotient(X2,quotient(X1,difference(X1,one)))) = product(quotient(one,X1),quotient(quotient(X2,X1),X1)),
inference(spm,[status(thm)],[c_0_184,c_0_208]) ).
cnf(c_0_214,plain,
quotient(quotient(product(product(X1,X2),X3),difference(X2,one)),quotient(X3,difference(X2,one))) = difference(X3,product(quotient(X3,difference(X2,one)),product(difference(X2,X1),X2))),
inference(spm,[status(thm)],[c_0_29,c_0_104]) ).
cnf(c_0_215,plain,
product(quotient(X1,difference(X1,one)),product(X2,X1)) = product(X1,product(X1,quotient(X2,difference(X1,one)))),
inference(spm,[status(thm)],[c_0_97,c_0_209]) ).
cnf(c_0_216,plain,
quotient(product(X1,X2),difference(X2,one)) = product(quotient(X1,quotient(one,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_210]),c_0_85]),c_0_28]) ).
cnf(c_0_217,plain,
difference(difference(X1,one),product(product(X1,quotient(one,X1)),X2)) = quotient(product(X1,product(X2,difference(X1,one))),difference(X1,one)),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_218,plain,
product(quotient(one,quotient(one,X1)),difference(X1,X2)) = product(quotient(one,X1),difference(difference(X1,one),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_211]),c_0_42]),c_0_14]) ).
cnf(c_0_219,plain,
difference(product(X1,X2),product(X3,quotient(X4,X1))) = quotient(difference(X2,product(difference(X1,X3),X4)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_67]),c_0_16]) ).
cnf(c_0_220,plain,
product(difference(difference(X1,one),one),difference(X1,X2)) = product(difference(X1,one),difference(quotient(one,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_212]),c_0_31]),c_0_98]) ).
cnf(c_0_221,plain,
product(quotient(one,X1),quotient(X2,difference(X1,one))) = product(product(quotient(one,X1),X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_215]),c_0_196]),c_0_26]),c_0_26]),c_0_216]),c_0_199]),c_0_25]),c_0_25]) ).
cnf(c_0_222,plain,
quotient(product(X1,product(difference(product(X1,quotient(one,X1)),X2),difference(X1,one))),difference(X1,one)) = difference(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_217,c_0_14]) ).
cnf(c_0_223,plain,
product(quotient(one,X1),difference(difference(X1,one),X2)) = product(X1,difference(difference(difference(X1,one),one),X2)),
inference(spm,[status(thm)],[c_0_218,c_0_31]) ).
cnf(c_0_224,plain,
quotient(difference(X1,product(difference(X2,one),X3)),X2) = difference(product(X2,X1),quotient(X3,X2)),
inference(spm,[status(thm)],[c_0_219,c_0_18]) ).
cnf(c_0_225,plain,
product(quotient(difference(difference(X1,X2),X3),X1),X2) = product(difference(X2,X1),product(quotient(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_32,c_0_106]) ).
cnf(c_0_226,plain,
difference(difference(X1,one),product(quotient(one,X1),X2)) = product(difference(X1,one),difference(quotient(one,X1),X2)),
inference(rw,[status(thm)],[c_0_200,c_0_220]) ).
cnf(c_0_227,plain,
product(difference(X1,one),difference(quotient(one,X1),X2)) = product(X1,difference(quotient(one,quotient(one,X1)),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_117]),c_0_28]),c_0_42]),c_0_24]),c_0_79]),c_0_24]),c_0_28]),c_0_42]),c_0_24]),c_0_79]),c_0_24]) ).
cnf(c_0_228,plain,
product(X1,difference(difference(difference(X1,one),one),X2)) = difference(product(X1,quotient(one,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_188]),c_0_134]),c_0_14]),c_0_16]),c_0_223]) ).
cnf(c_0_229,plain,
difference(quotient(X1,difference(X1,one)),quotient(X2,X1)) = difference(X1,quotient(difference(X1,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_204]),c_0_31]),c_0_23]),c_0_143]),c_0_90]) ).
cnf(c_0_230,plain,
quotient(product(X1,difference(quotient(one,X1),X2)),X1) = product(X1,quotient(product(X1,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_204]),c_0_24]),c_0_28]),c_0_24]) ).
cnf(c_0_231,plain,
quotient(difference(difference(difference(X1,one),one),X2),X1) = product(product(difference(X1,one),X2),quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_81]),c_0_65]),c_0_14]),c_0_79]) ).
cnf(c_0_232,plain,
difference(difference(X1,one),product(quotient(one,X1),X2)) = product(X1,difference(quotient(one,quotient(one,X1)),X2)),
inference(rw,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_233,negated_conjecture,
product(x0,product(eta(x0),x1)) != product(j(j(x0)),x1),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_234,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(c_0_235,plain,
difference(X1,difference(product(X1,quotient(one,X1)),X2)) = difference(difference(difference(X1,one),one),X2),
inference(spm,[status(thm)],[c_0_26,c_0_228]) ).
cnf(c_0_236,plain,
difference(X1,quotient(difference(quotient(one,X1),X2),X1)) = product(X1,quotient(product(quotient(one,X1),X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_106]),c_0_96]),c_0_27]),c_0_157]),c_0_231]),c_0_173]),c_0_57]),c_0_24]),c_0_26]) ).
cnf(c_0_237,plain,
difference(difference(difference(X1,one),one),product(X1,X2)) = product(X1,difference(quotient(one,quotient(one,X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_31]),c_0_227]) ).
cnf(c_0_238,negated_conjecture,
product(x0,product(eta(x0),x1)) != product(j(j(x0)),x1),
c_0_233 ).
cnf(c_0_239,plain,
eta(X1) = product(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_234,c_0_20]) ).
cnf(c_0_240,plain,
product(X1,difference(quotient(one,quotient(one,X1)),X2)) = product(product(X1,quotient(one,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_146]),c_0_236]),c_0_53]),c_0_237]) ).
cnf(c_0_241,negated_conjecture,
product(x0,product(product(difference(x0,one),x0),x1)) != product(quotient(one,quotient(one,x0)),x1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_238,c_0_21]),c_0_21]),c_0_239]) ).
cnf(c_0_242,plain,
quotient(product(product(X1,quotient(one,X1)),X2),X1) = product(X1,quotient(product(quotient(one,X1),X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_240]),c_0_31]),c_0_27]),c_0_31]),c_0_236]) ).
cnf(c_0_243,negated_conjecture,
product(x0,product(product(x0,quotient(one,x0)),x1)) != product(quotient(one,quotient(one,x0)),x1),
inference(rw,[status(thm)],[c_0_241,c_0_27]) ).
cnf(c_0_244,plain,
product(X1,product(product(X1,quotient(one,X1)),X2)) = product(quotient(one,quotient(one,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_242]),c_0_53]),c_0_170]) ).
cnf(c_0_245,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_243,c_0_244])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP764-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/1.81 % Computer : n010.cluster.edu
% 0.12/1.81 % Model : x86_64 x86_64
% 0.12/1.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/1.81 % Memory : 8046.5625MB
% 0.12/1.81 % OS : Linux 6.8.0-71-generic
% 0.12/1.81 % CPULimit : 300
% 0.12/1.81 % WCLimit : 300
% 0.12/1.81 % DateTime : Sun Sep 20 20:38:45 UTC 2026
% 0.12/1.82 % CPUTime :
% 0.12/1.82 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/1.86 Running first-order theorem proving
% 0.12/1.86 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.78/8.57 % Version: 3.5.1
% 45.78/8.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 45.78/8.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 45.78/8.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 45.78/8.57 % Starting new_bool_3 with 300s (1) cores
% 45.78/8.57 % Starting new_bool_1 with 300s (1) cores
% 45.78/8.57 % Starting sh5l with 300s (1) cores
% 45.78/8.57 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3479962 completed with status 0
% 45.78/8.57 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 45.78/8.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 45.78/8.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 45.78/8.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 45.78/8.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 45.78/8.57 % No SInE strategy applied
% 45.78/8.57 % Search class: FUUPM-FFSF22-MFFFFFNN
% 45.78/8.57 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 45.78/8.57 % Starting SubtermCWHack with 136s (1) cores
% 45.78/8.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 45.78/8.57 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 45.78/8.57 % Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 45.78/8.57 % Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 45.78/8.57 % E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with pid 3479969 completed with status 0
% 45.78/8.57 % Result found by E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S
% 45.78/8.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 45.78/8.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 45.78/8.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 45.78/8.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 45.78/8.57 % No SInE strategy applied
% 45.78/8.57 % Search class: FUUPM-FFSF22-MFFFFFNN
% 45.78/8.57 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 45.78/8.57 % Starting SubtermCWHack with 136s (1) cores
% 45.78/8.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 45.78/8.57 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 45.78/8.57 % Preprocessing time : 0.001 s
% 45.78/8.57 % Presaturation interreduction done
% 45.78/8.57
% 45.78/8.57 % Proof found!
% 45.78/8.57 % SZS status Unsatisfiable
% 45.78/8.57 % SZS output start CNFRefutation
% See solution above
% 45.78/8.57 % Parsed axioms : 13
% 45.78/8.57 % Removed by relevancy pruning/SinE : 0
% 45.78/8.57 % Initial clauses : 13
% 45.78/8.57 % Removed in clause preprocessing : 3
% 45.78/8.57 % Initial clauses in saturation : 10
% 45.78/8.57 % Processed clauses : 4003
% 45.78/8.57 % ...of these trivial : 2520
% 45.78/8.57 % ...subsumed : 252
% 45.78/8.57 % ...remaining for further processing : 1231
% 45.78/8.57 % Other redundant clauses eliminated : 0
% 45.78/8.57 % Clauses deleted for lack of memory : 0
% 45.78/8.57 % Backward-subsumed : 0
% 45.78/8.57 % Backward-rewritten : 298
% 45.78/8.57 % Generated clauses : 287750
% 45.78/8.57 % ...of the previous two non-redundant : 212359
% 45.78/8.57 % ...aggressively subsumed : 0
% 45.78/8.57 % Contextual simplify-reflections : 0
% 45.78/8.57 % Paramodulations : 287750
% 45.78/8.57 % Factorizations : 0
% 45.78/8.57 % NegExts : 0
% 45.78/8.57 % Equation resolutions : 0
% 45.78/8.57 % Disequality decompositions : 0
% 45.78/8.57 % Total rewrite steps : 1270381
% 45.78/8.57 % ...of those cached : 1227421
% 45.78/8.57 % Propositional unsat checks : 0
% 45.78/8.57 % Propositional check models : 0
% 45.78/8.57 % Propositional check unsatisfiable : 0
% 45.78/8.57 % Propositional clauses : 0
% 45.78/8.57 % Propositional clauses after purity: 0
% 45.78/8.57 % Propositional unsat core size : 0
% 45.78/8.57 % Propositional preprocessing time : 0.000
% 45.78/8.57 % Propositional encoding time : 0.000
% 45.78/8.57 % Propositional solver time : 0.000
% 45.78/8.57 % Success case prop preproc time : 0.000
% 45.78/8.57 % Success case prop encoding time : 0.000
% 45.78/8.57 % Success case prop solver time : 0.000
% 45.78/8.57 % Current number of processed clauses : 923
% 45.78/8.57 % Positive orientable unit clauses : 921
% 45.78/8.57 % Positive unorientable unit clauses: 2
% 45.78/8.57 % Negative unit clauses : 0
% 45.78/8.57 % Non-unit-clauses : 0
% 45.78/8.57 % Current number of unprocessed clauses: 207168
% 45.78/8.57 % ...number of literals in the above : 207168
% 45.78/8.57 % Current number of archived formulas : 0
% 45.78/8.57 % Current number of archived clauses : 311
% 45.78/8.57 % Clause-clause subsumption calls (NU) : 0
% 45.78/8.57 % Rec. Clause-clause subsumption calls : 0
% 45.78/8.57 % Non-unit clause-clause subsumptions : 0
% 45.78/8.57 % Unit Clause-clause subsumption calls : 17
% 45.78/8.57 % Rewrite failures with RHS unbound : 0
% 45.78/8.57 % BW rewrite match attempts : 4483
% 45.78/8.57 % BW rewrite match successes : 251
% 45.78/8.57 % Condensation attempts : 0
% 45.78/8.57 % Condensation successes : 0
% 45.78/8.57 % Termbank termtop insertions : 8256706
% 45.78/8.57 % Search garbage collected termcells : 2
% 45.78/8.57
% 45.78/8.57 % -------------------------------------------------
% 45.78/8.57 % User time : 6.273 s
% 45.78/8.57 % System time : 0.208 s
% 45.78/8.57 % Total time : 6.481 s
% 45.78/8.57 % Maximum resident set size: 3636 pages
% 45.78/8.57
% 45.78/8.57 % -------------------------------------------------
% 45.78/8.57 % User time : 31.162 s
% 45.78/8.57 % System time : 1.209 s
% 45.78/8.57 % Total time : 32.371 s
% 45.78/8.57 % Maximum resident set size: 4864 pages
% 45.78/8.57 % E exiting
%------------------------------------------------------------------------------